Cumulant Lattice Boltzmann Method Research Articles

Under-resolved and large eddy simulations of a decaying Taylor\u2013Green vortex with the cumulant lattice Boltzmann method

We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ({hbox {Re}}=160{,}000) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

Simulation of turbulent bubbly pipe flow with high density ratio and high reynolds number by using the lattice boltzmann method and a multi-phase field model

Direct numerical simulation (DNS) has been widely employed to study the dynamics of turbulent bubbly flows; however, it is used in a limited setting, namely, turbulent bubbly channel flows with low density ratio and low Reynolds number. The present study aims to overcome these limitations and simulate turbulent bubbly pipe flow of a water-air system, a common experimental setting, with high density ratio and Reynolds number. Recently, we developed a cumulant lattice Boltzmann method for two-phase flows and simulated violent two-phase flows with high density ratio and high Reynolds number (Sitompul and Aoki, 2019). In this study, that method is extended by incorporating a multi-phase field model for simulating dispersed bubbles. The proposed method was evaluated by using several cases, namely, 3D bubble rising, turbulent single-phase channel and pipe flows with friction Reynolds number (Reτ≈180,550), turbulent bubbly channel flows with (Reτ≈180) and void fraction (α=1.5%,19.4%), and turbulent bubbly pipe flow with (Reτ=550,α=9.5%). The proposed method can stably simulate the cases, and the results obtained by the proposed method agree well with numerical and experimental results given in the references for given computational domain and grid sizes.

Actuator line simulations of wind turbine wakes using the lattice Boltzmann method

Abstract. The high computational demand of large-eddy simulations (LESs) remains the biggest obstacle for a wider applicability of the method in the field of wind energy. Recent progress of GPU-based (graphics processing unit) lattice Boltzmann frameworks provides significant performance gains alleviating such constraints. The presented work investigates the potential of LES of wind turbine wakes using the cumulant lattice Boltzmann method (CLBM). The wind turbine is represented by the actuator line model (ALM). The implementation is validated and discussed by means of a code-to-code comparison to an established finite-volume Navier–Stokes solver. To this end, the ALM is subjected to both laminar and turbulent inflow while a standard Smagorinsky sub-grid-scale model is employed in the two numerical approaches. The resulting wake characteristics are discussed in terms of the first- and second-order statistics as well the spectra of the turbulence kinetic energy. The near-wake characteristics in laminar inflow are shown to match closely with differences of less than 3 % in the wake deficit. Larger discrepancies are found in the far wake and relate to differences in the point of the laminar-turbulent transition of the wake. In line with other studies, these differences can be attributed to the different orders of accuracy of the two methods. Consistently better agreement is found in turbulent inflow due to the lower impact of the numerical scheme on the wake transition. In summary, the study outlines the feasibility of wind turbine simulations using the CLBM and further validates the presented set-up. Furthermore, it highlights the computational potential of GPU-based LBM implementations for wind energy applications. For the presented cases, near-real-time performance was achieved using a single, off-the-shelf GPU on a local workstation.

The Actuator Line Model in Lattice Boltzmann Frameworks: Numerical Sensitivity and Computational Performance

The growing use of large-eddy simulations for the modelling of wind farms makes the need for efficient numerical frameworks more essential than ever. GPU-accelerated implementations of the Lattice Boltzmann Method (LBM) have shown to provide significant performance gains over classical Navier-Stokes-based computational fluid dynamics. Yet, their use in the field of wind energy remains limited to date. In this fundamental study the cumulant LBM is scrutinised for actuator line simulations of wind turbines. The numerical sensitivity of the method in a simple uniform inflow is investigated with respect to spatial and temporal resolution as well as the width of the actuator line’s regularisation kernel. Comparable accuracy and slightly better stability properties are shown in relation to a standard Navier-Stokes implementation. The results indicate the overall suitability of the cumulant LBM for wind turbine wake simulations. The potential of the LBM for future wind energy applications is clarified by means of a brief comparison of computational performance.

A filtered cumulant lattice Boltzmann method for violent two-phase flows

The Lattice Boltzmann Method (LBM) has been successfully applied to simulate various two-phase flow problems such as Rayleigh-Taylor instability, rising bubble, and droplet dynamics. However, the method, known as two-phase LBM, faces difficulty in simulating violent two-phase flow problems such as dam-breaking and liquid jet breakup where the density ratio and Reynolds number are high, and there are rapid and complex topological changes. In this paper, we address the problem by using a filtered cumulant LBM. The incompressible two-phase flow equations are solved by using a velocity-based formulation of two-phase LBM with a cumulant collision model to stably simulate problems with high density ratio and Reynolds number. There is no pressure iteration in this formulation and we can keep the simplicity of the cumulant model. To further enhance the stability in violent flows, a second order filter is applied on the velocity field which can be turned off for non-violent flows. For interface capturing, a conservative phase-field LBM which guarantees the mass conservation is employed. The proposed method is first validated using five non-violent flow problems and the results are in good agreements with experimental and computational references. The proposed method is then employed to solve three violent flow problems and the results are in qualitatively good agreements with experimental and computational references. The proposed method is more diffusive than the unfiltered model but is stable for all problems simulated in this paper. These results can be used as a preliminary study on violent two-phase flow simulation using two-phase LBM.

Towards real-time simulation of turbulent air flow over a resolved urban canopy using the cumulant lattice Boltzmann method on a GPGPU

This work explores the feasibility of real-time large-eddy simulations of flow over urban canopies at the neighborhood scale. The cumulant lattice Boltzmann method is employed using a single General Purpose Graphic Processing Unit (GPGPU). In order to demonstrate the validity and efficiency of this approach we simulate wind flow in a neighborhood of Basel. Simulation results are validated against measurements from the Basel Urban Boundary Layer Experiment (BUBBLE) and are compared to previous CFD simulations. Turbulence statistics are found to be in agreement with corresponding tower measurements according to several validation metrics. While quantitative comparisons are limited to the six measurement locations of the field measurements, the available data supports the conjecture that real-time simulation of urban air flow is feasible at the neighborhood scale with the proposed numerical technique.

Towards overcoming the LES crisis

ABSTRACTIndustrial large-eddy simulation (LES), i.e. overnight runs with degrees of freedom (DOFs) and timesteps, has been one of the top priorities of CFD research over the last two decades. Current network and solver timings indicate that the required target of 5 ms/timestep is within reach: some cumulant Lattice Boltzmann Method (LBM) codes are reporting speeds in this range using multi-GPU systems, while some Finite Difference Method (FDM) codes running on traditional CPUs are achieving speeds that are only a factor of 2–4 slower. This implies that the long wait may be coming to a close. During the last three decades, a number of promising approaches have been tried. Given that the majority of these were promoted as the ‘solution to LES’ or the ‘solution to turbulence’, the paper lists them under the label of ‘the false prophecies’. Furthermore, some of the assumptions that are always part of the scientific discovery process turned out to be incorrect. These are listed under the term 'the false assumptions'. From an informal survey conducted in January of 2018, it appears that simple Cartesian Finite Difference codes or, equivalently, Lattice Boltzmann codes may be the first to achieve industrial LES.

Multiscale simulation of turbulent flow interacting with porous media based on a massively parallel implementation of the cumulant lattice Boltzmann method

Flow noise during takeoff and landing of commercial aircrafts can be substantially reduced by the use of porous surface layers in suitable sections of wing profiles. On the other hand (passive) porosity and roughness of surfaces tend to have an adverse effect on the boundary layer and thus on the lift of wings. This results in the need to be able to predict the aerodynamic effects of porous segments of the surface by numerical methods for aerodynamic design of wings, taking into account porosity and roughness as a function of Reynolds number. The application of the RANS equations for this task requires additional modeling terms such as the permeability and the Kozeny–Carman parameter as well as the turbulent fluctuations of the velocity field to be determined by Direct Numerical Simulation (DNS) / Large Eddy Simulation (LES) simulations based on the lattice Boltzmann method which is the main focus of this contribution. For the simulation of the flow at the pore scale we use the cumulant lattice Boltzmann method. Due to the inherent requirements of resolving both the turbulence on the scale of an airfoil and the flow inside the pore scale resolved porous medium the resulting simulations require more than a billion grid nodes on a refined three-dimensional mesh leading to massively parallel simulations. We discuss modeling and computational aspects of our approach and present computational results including experimental validations.

Near-wall treatment for the simulation of turbulent flow by the cumulant lattice Boltzmann method

We present a new wall function implementation for the cumulant lattice Boltzmann method that sets a partial slip velocity on the wall by computing a skin frictional coefficient. Our approach uses local information and is particularly appropriate for implementations on general purpose graphics processing units. The validation of the model has been conducted by performing numerical simulations of the turbulent channel flow test case with different grid resolutions and for different Reynolds numbers. The results showed encouraging agreement with Direct Numerical Simulation data for velocity profile, Reynolds shear and normal stresses.

Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part I: Derivation and validation

The cumulant lattice Boltzmann method offers a set off free relaxation parameters that do not influence the result at leading order but can be used to influence the leading error. Using Taylor expansion we derive exact functional relationships for the elimination of the linearized leading error of the method. The diffusion term in the Navier–Stokes equation becomes fourth order accurate for small enough viscosity with these parameters. The result is general and does not depend on the flow. The analytical solution is tested against Taylor–Green vortex flow and shear wave flow and fourth order accuracy for the diffusion is observed.

Parametrization of the cumulant lattice Boltzmann method for fourth order accurate diffusion part II: Application to flow around a sphere at drag crisis

The optimized cumulant lattice Boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to Reynolds number 106. The drag crisis is well captured by the method. We demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions. The intermediate values of drag in a small range of Reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions. Around the critical Reynolds number, the time spent in the low drag condition increases with the Reynolds number such that the average drag curve has a finite steepness.

Implicit Large Eddy Simulation of Flow in a Micro-Orifice with the Cumulant Lattice Boltzmann Method

A detailed numerical study of turbulent flow through a micro-orifice is presented in this work. The flow becomes turbulent due to the orifice at the considered Reynolds numbers (∼ 10 4 ). The obtained flow rates are in good agreement with the experimental measurements. The discharge coefficient and the pressure loss are presented for two input pressures. The laminar stress and the generated turbulent stresses are investigated in detail, and the location of the vena contracta is quantitatively reproduced.

Simulation of micro aggregate breakage in turbulent flows by the cumulant lattice Boltzmann method

The production of nano-particles from larger aggregates is an important industrial process, especially for life-science products. A micro-machined disperser is studied numerically by the cumulant lattice Boltzmann method. The aggregates are modeled as tracer particles with mass and drag coefficient. They record the history of the experienced stresses and the relative velocity of aggregates with respect to the fluid. The tracer particles are implemented in a massively parallel multi-resolution lattice Boltzmann framework. In this paper, the effect of fractal dimension and the number of primary particles on the breakage of aggregates due to the relative velocities of the particles with respect to the surrounding fluid are investigated. It is found that aggregates with realistic geometry (fractal number 1.85) usually have Stokes numbers smaller than one such that the load on these aggregates is dominated by the strain rate in the surrounding fluid. This is in contrast to spherical particles (fractal number 3) that have larger Stokes numbers exceeding one such that the load from their relative velocity with respect to the surrounding fluid is not negligible.

Distributed cumulant lattice Boltzmann simulation of the dispersion process of ceramic agglomerates

The dispersion process of ceramic agglomerates modeled as solid particles with mass and drag coefficient in a micro-machined disperser is simulated with the cumulant lattice Boltzmann method (LBM). A simplified particle model is used for tracking the pathlines by compact quadratic interpolation. Th e simulation of the disperser is validated with experimental data. The simulation is found to be in quantitative agreement with both PIV measurements and flow rate measurements. Pathlines record the complete history of the strain rate each particle suffers during its passage. It is assumed that agglomerates break-up when they experience strain rates above a critical threshold. The obtained data for the maximum strain can be condensed into a simple exponential model with only two parameters that are determined by the simulation results. This condensed model is used to determine the probability that the particle experience a given threshold strain rate after a given number of passages through the disperser.